# Measuring the Size of Large No-Limit Poker Games

arXiv: https://arxiv.org/abs/1302.7008 · HTML: https://mlsanity.com/paper/1302.7008/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 15 of 15)

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- [Search in Imperfect Information Games](https://mlsanity.com/paper/2111.05884/) (2021)
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- [SpinGPT: A Large-Language-Model Approach to Playing Poker Correctly](https://mlsanity.com/paper/2509.22387/) (2025)
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- [AV-AIVAT: 74x Cheaper Agent Evaluation with Certified Anytime-Valid Stopping in Imperfect-Information Games](https://mlsanity.com/paper/2608.06362/) (2026)
- [Abstraction Agent](https://mlsanity.com/paper/2609.04303/) (2026)
- [DecisionHoldem: Safe Depth-Limited Solving With Diverse Opponents for Imperfect-Information Games](https://mlsanity.com/paper/2201.11580/) (2022)
- [No-Regret Strategy Solving in Imperfect-Information Games via Pre-Trained Embedding](https://mlsanity.com/paper/2511.12083/) (2025)
- [Domain-Independent Game Abstraction using Word Embedding Techniques](https://mlsanity.com/paper/2605.15543/) (2026)
- [Learning to Play: Reinforcement Learning and Games](https://mlsanity.com/paper/2610.17391/) (2026)

## Abstract (arXiv)

In the field of computational game theory, games are often compared in terms of their size. This can be measured in several ways, including the number of unique game states, the number of decision points, and the total number of legal actions over all decision points. These numbers are either known or estimated for a wide range of classic games such as chess and checkers. In the stochastic and imperfect information game of poker, these sizes are easily computed in "limit" games which restrict the players' available actions, but until now had only been estimated for the more complicated "no-limit" variants. In this paper, we describe a simple algorithm for quickly computing the size of two-player no-limit poker games, provide an implementation of this algorithm, and present for the first time precise counts of the number of game states, information sets, actions and terminal nodes in the no-limit poker games played in the Annual Computer Poker Competition.